"They learn from us the newest experience of the hybrid war against Russia," Ukrainian President Petro Poroshenko told CBS News. "And we learn from them their tactics and strategy, which makes my army much more efficient."

Poroshenko wants more weapons from the U.S., and UN peacekeepers. He says his country is the front line in a new Cold War with Russia.

Ukrainian leader on "hot war" with russia

"They want to have Soviet Union back," Poroshenko said, adding that he believes Vladimir Putin, who was sworn in Monday for his fourth term as Russian President, wants to reconquer Ukraine and rebuild the "Russian Empire."

Ukraine says thousands of Russians are fighting in the east, alongside the rebels. Moscow has repeatedly denied it's involved in the conflict

But Col. Dennis Deeley, who leads the American trainers in Ukraine, is also reminded of the Cold War. The Ukrainians use old Soviet-era tanks -- the type the Russian enemy used when he served in Europe in the 1980s.

With U.S. backing, Estonia tells Russia "we are ready to fight"

"When you come around the corner and you see a tank, a Russian tank, a T-64 tank, its barrel pointed at you -- it makes you hesitate for a second as you come around the corner in your vehicle," Deeley said.

The Cold War ended in 1991, but now Ukraine's dangerous conflict once again pits Russia against the West.